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What proportion of students at your school use Titter? To find out, you survey a simple random sample of students from the school roster.

Which of the following is a true statement about the sample result?

A)The survey result will be biased due to voluntary response bias.

B)The survey result will be biased due to undercoverage.

C)An SRS of 100 students is more likely than an SRS of 50 students to get a sample result close to the true population value.

D)An SRS of 50 students is more likely than an SRS of 100 students to get a sample result close to the true population value.

E)The survey result will be free from bias because a simple random sample was selected.

User Earizon
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1 Answer

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The true statement about survey results from a simple random sample (SRS) is that an SRS of 100 students is more likely than an SRS of 50 students to get a sample result close to the true population value, as larger samples tend to be more representative of the population.

The survey result will not necessarily be free from bias just because a simple random sample (SRS) was selected as various forms of bias can still occur in SRS as well. For example, if certain groups of students are less likely to respond or are unavailable during the time of the survey, the result could still be biased.

However, between the options provided, the most accurate statement is that:

C) An SRS of 100 students is more likely than an SRS of 50 students to get a sample result close to the true population value.

This statement is based on the idea that larger samples tend to produce more precise estimates of population parameters when compared to smaller samples, assuming both samples are randomly selected with the same technique. Intuitively, sampling more individuals gives us more information and tends to yield a result that is closer to the true characteristic of the entire population.

However, this doesn't guarantee the absence of bias, but it does increase the probability of having a more representative and accurate result.

User Nocebo
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